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101 LearnersLast updated on April 28th, 2025
Cube Root of 74088000
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 74088000 and explain the methods used.
What is the Cube Root of 74088000?
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.
In exponential form, ∛74088000 is written as 74088000(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 74088000, then y3 can be 74088000. The cube root of 74088000 is an exact value, which is 420.
Finding the Cube Root of 74088000
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 74088000. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Estimation method
- Subtraction method
- Halley’s method
Since 74088000 is a perfect cube, we can use the prime factorization method or estimation method.
Cube Root of 74088000 by Prime Factorization
Let's find the cube root of 74088000 using the prime factorization method.
First, we factorize 74088000 into its prime factors: 74088000 = 26 × 32 × 53 × 73
To find the cube root, we take the cube root of each factor: ∛(26 × 32 × 53 × 73)
= 2(6/3) × 3(2/3) × 5(3/3) × 7(3/3)
22 × 3(2/3) × 5 × 7
4 × (3(2/3)) × 5 × 7
4 × 3 × 5 × 7 = 420
The cube root of 74088000 is 420.
Common Mistakes and How to Avoid Them in the Cube Root of 74088000
Cube Root of 74088000 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 74088000 cubic centimeters. Find the length of one side of the container equal to its cube root.
Explanation
Problem 2
A company manufactures 74088000 cubic meters of material. Calculate the amount of material left after using 20000000 cubic meters.
Explanation
Problem 3
A tank holds 74088000 cubic meters of water. Another tank holds 10000000 cubic meters. What would be the total volume if the tanks are combined?
Explanation
Problem 4
When the cube root of 74088000 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
Explanation
Problem 5
Find ∛(37044000 + 37044000).
Explanation
FAQs on 74088000 Cube Root
1.Can we find the Cube Root of 74088000?
2.Why is Cube Root of 74088000 a whole number?
3.Is it possible to get the cube root of 74088000 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
Important Glossaries for Cube Root of 74088000
- Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. For example: 5 × 5 × 5 = 125, therefore, 125 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 74088000(1/3), ⅓ is the exponent which denotes the cube root.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Prime factorization: A method used to express a number as a product of its prime factors, particularly helpful in finding cube roots of perfect cubes.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
